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Mathematics 21 Online
OpenStudy (theraggedydoctor):

Four signal flags - one red, one blue, one yellow, and one green - can be arranged from top to bottom on a signal pole. Every arrangement of the four flags is a different signal. How many different signals using all four flags have the red flag on top?

OpenStudy (sleepyhead314):

four flags times three switchable colors 4 * 3 = answer (I think, I may not be the best at probability, sorry)

OpenStudy (theraggedydoctor):

Why three...?

OpenStudy (theraggedydoctor):

@sleepyhead314

OpenStudy (sleepyhead314):

red is stuck the other THREE colors get to move around

OpenStudy (theraggedydoctor):

Alright, but 12 isn't an answer. I thought since it was one red, one blue, one yellow, and one green, four times, you'd have to multiply \(4 \times \ 4\).

OpenStudy (sleepyhead314):

right sorry I just tried it the long way... RBYG RBGY RYGB RYBG RGBY RGYB 6 combinations same idea that since red is stuck only 3 can move but mathematically that would be represented by 3! or 3 factorial = 3 * 2 * 1 = answer

OpenStudy (theraggedydoctor):

So the answer is 6.

OpenStudy (sleepyhead314):

yes

OpenStudy (theraggedydoctor):

Thank you. c:

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